Split general quasi-variational inequality problem

AbstractIn this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of a split variational inequality problem, quasivariational and variational inequality problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for a split general quasi-variational inequality problem and discuss some special cases. Further, we discuss the convergence criteria of these iterative algorithms. The results presented in this paper generalize, unify and improve many previously known results for quasi-variational and variational inequality problems.

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Split General Strong Nonlinear Quasi-Variational Inequality Problem

Mathematical Problems in Engineering ◽

10.1155/2016/5937016 ◽

2016 ◽

Vol 2016 ◽

pp. 1-6

Author(s):

Yali Zhao ◽

Dongxue Han

Keyword(s):

Variational Inequality ◽

Iterative Algorithm ◽

Variational Inequality Problem ◽

Natural Extension ◽

Variational Inequality Problems ◽

Convergence Criteria ◽

Inequality Problem ◽

Strongly Nonlinear ◽

Quasi Variational Inequality ◽

Split Variational Inequality Problem

We introduce a split general strong nonlinear quasi-variational inequality problem which is a natural extension of a split general quasi-variational inequality problem, split variational inequality problem, and quasi-variational and variational inequality problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for the split general strongly nonlinear quasi-variational inequality problem and discuss the convergence criteria of the iterative algorithm. The results presented here generalized, unify, and improve many previously known results for quasi-variational and variational inequality problems.

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Existence Results for Vector Mixed Quasi-Complementarity Problems

Journal of Mathematics ◽

10.1155/2013/204348 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Suhel Ahmad Khan ◽

Naeem Ahmad

Keyword(s):

Variational Inequality ◽

Banach Spaces ◽

Variational Inequality Problem ◽

Existence Of Solutions ◽

Complementarity Problems ◽

Existence Results ◽

Variational Inequality Problems ◽

Inequality Problem ◽

Quasi Variational Inequality

We introduce strong vector mixed quasi-complementarity problems and the corresponding strong vector mixed quasi-variational inequality problems. We establish equivalence between strong mixed quasi-complementarity problems and strong mixed quasi-variational inequality problem in Banach spaces. Further, using KKM-Fan lemma, we prove the existence of solutions of these problems, under pseudomonotonicity assumption. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature.

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On the $O(1/k)$ Convergence Rate of He's Alternating Directions Method for a Kind of Structured Variational Inequality Problem

Journal of Mathematics Research ◽

10.5539/jmr.v7n2p69 ◽

2015 ◽

Vol 7 (2) ◽

pp. 69

Author(s):

Haiwen Xu

Keyword(s):

Variational Inequality ◽

Convergence Rate ◽

Variational Inequality Problem ◽

Variational Inequality Problems ◽

System Of Nonlinear Equations ◽

Inequality Problem ◽

Quadratic Minimization ◽

Projection And Contraction Methods ◽

Monotone Variational Inequality ◽

Alternating Directions Method

The alternating directions method for a kind of structured variational inequality problem (He, 2001) is an attractive method for structured monotone variational inequality problems. In each iteration, the subproblemsare convex quadratic minimization problem with simple constraintsand a well-conditioned system of nonlinear equations that can be efficiently solvedusing classical methods. Researchers have recently described the convergence rateof projection and contraction methods for variational inequality problems andthe original ADM and its linearized variant. Motivated and inspired by researchinto the convergence rate of these methods, we provide a simple proof to show the $O(1/k)$ convergencerate of alternating directions methods for structured monotone variational inequality problems (He, 2001).

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